Symmetric and skew-symmetric {0, ±1} - matrices with large determinants
We show that the existence of {±}-matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular, we prove a recent conjecture of Armario. We also show that large submatrices of conference matrices are determined by their spectrum.
Saved in:
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/144977 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| id |
sg-ntu-dr.10356-144977 |
|---|---|
| record_format |
dspace |
| spelling |
sg-ntu-dr.10356-1449772023-02-28T19:52:50Z Symmetric and skew-symmetric {0, ±1} - matrices with large determinants Greaves, Gary Suda, Sho School of Physical and Mathematical Sciences Mathematics - Combinatorics Mathematics - Combinatorics Science::Mathematics D‐optimal Design EW Matrix We show that the existence of {±}-matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular, we prove a recent conjecture of Armario. We also show that large submatrices of conference matrices are determined by their spectrum. Accepted version 2020-12-07T07:27:00Z 2020-12-07T07:27:00Z 2016 Journal Article Greaves, G., & Suda, S. (2017). Symmetric and Skew-Symmetric {0,±1}-Matrices with Large Determinants. Journal of Combinatorial Designs, 25(11), 507–522. doi:10.1002/jcd.21567 1063-8539 https://hdl.handle.net/10356/144977 10.1002/jcd.21567 11 25 507 522 en Journal of Combinatorial Designs This is the accepted version of the following article: Greaves, G., & Suda, S. (2017). Symmetric and Skew-Symmetric {0,±1}-Matrices with Large Determinants. Journal of Combinatorial Designs, 25(11), 507–522., which has been published in final form at 10.1002/jcd.21567. This article may be used for non-commercial purposes in accordance with the Wiley Self-Archiving Policy [https://authorservices.wiley.com/authorresources/Journal-Authors/licensing/self-archiving.html]. application/pdf |
| institution |
Nanyang Technological University |
| building |
NTU Library |
| continent |
Asia |
| country |
Singapore Singapore |
| content_provider |
NTU Library |
| collection |
DR-NTU |
| language |
English |
| topic |
Mathematics - Combinatorics Mathematics - Combinatorics Science::Mathematics D‐optimal Design EW Matrix |
| spellingShingle |
Mathematics - Combinatorics Mathematics - Combinatorics Science::Mathematics D‐optimal Design EW Matrix Greaves, Gary Suda, Sho Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| description |
We show that the existence of {±}-matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular, we prove a recent conjecture of Armario. We also show that large submatrices of conference matrices are determined by their spectrum. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Greaves, Gary Suda, Sho |
| format |
Article |
| author |
Greaves, Gary Suda, Sho |
| author_sort |
Greaves, Gary |
| title |
Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title_short |
Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title_full |
Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title_fullStr |
Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title_full_unstemmed |
Symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| title_sort |
symmetric and skew-symmetric {0, ±1} - matrices with large determinants |
| publishDate |
2020 |
| url |
https://hdl.handle.net/10356/144977 |
| _version_ |
1759854562730049536 |